Question

The task involves writing a C++ program that determines the prime numbers between 1 and 100. The steps you should follow to identify the prime numbers are the following. 1. The number 1 is not a prime number, so it should be scratched. 2. Starting from the first prime number, which is 2, you scratch all the numbers that are the multiple of 2. You should not scratch out 2 itself. 3. The next number in the sequence after the previous step is 3, which is a prime number itself. Now scratch out all the numbers the multiple of 3. 4. The next number should be 5, which is again, a prime number. Scratch all the multiple of 5, but not 5 itself. Repeat the steps until no more prime numbers available. 5. The initial table before the steps are taken: 2 3 5 8 10 20 1 4 6 7 12 13 16 18 19 11 14 15 17 21 31 22 23 33 24 25 35 26 36 27 28 38 29 39 30 40 32 42 34 37 43 44 54 45 46 56 48 49 59 50 60 41 47 52 53 51 55 57 58 62 72 68 78 88 63 73 83 66 76 86 69 79 89 70 80 90 61 64 65 67 74 84 94 71 75 77 81 82 85 87 91 92 93 95 96 97 98 99 100 The resulting table after the prime numbers are determined: 2 3 5 7 12 13 23 19 29 11 17 21 25 е 31 41 32 35 37 47 43 52 51 53 59 е 61 67 73 83 71 72 79 81 85 89 e 91 92 95 97

Answer 1

C++ Code:

#include <iostream>
#include <fstream>
#include <iomanip>

using namespace std;

const int N = 10;//Dimension of table (n x n)

//Function to find primes in the table
void findPrimes(int table[N][N]){
    //Special case for 1
    table[0][0] = 0;
    bool primeFound = true;
    int prime = 2;// First prime number
    int nextPrime = 0;
    while(primeFound){
        primeFound = false;
        //Check table for all multiples of current prime
        for(int i = 0; i < N; i++){
            for(int j = 0; j < N; j++){
                //If number in table is multiple of current prime then set it as 0
                if(table[i][j] != prime && table[i][j] != 0 && table[i][j] % prime == 0)
                    table[i][j] = 0;
                
                //Find next prime number
                if(!nextPrime && table[i][j] > prime && table[i][j] != 0) {
                    nextPrime = table[i][j];
                    primeFound = true;//Prime number found in this check
                }
            }
        }
        prime = nextPrime;//Set next prime to be current prime
    }
}

//Function to print table on console
void printTable(int table[N][N]){
    for(int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            cout << left << setw(5) << table[i][j];
        }
        cout << "\n";
    }
    cout << endl;
}

//Function to save table in a file
void saveTable(int table[N][N]){
    ofstream out("primes.txt");//Open file to write output
    for(int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            out << left << setw(5) << table[i][j] << " ";
        }
        out << "\n";
    }
    out.close();//Close the file
}

int main(int argc, char *argv[]) {
    int table[N][N];// 10x10 = 100

    //Fill the table
    for(int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
            table[i][j] = i*N + j + 1;

    cout << "The initial table before the steps are taken:\n";
    printTable(table);//Print table

    findPrimes(table);//Find primes in the table

    cout << "The resulting table after the prime numbers are determined:\n";
    printTable(table);//Print table

    saveTable(table);//Save table in a file

    return 0;
}

Console output:

The initial table before the steps are taken: 1 2 3 4 5 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 The resulting table after the prime numbers are determined: 10 2 3 C C 7 C 0 0 11 C 13 0 10 C 17 C 19 0 0 0 23 0 25 0 10 0 29 C 31 0 0 0 35 C 37 C C 0 41 0 43 0 0 C 47 C 49 0 0 0 53 0 0 C 0 59 C 61 0 C 0 65 0 67 0 0 10 79 71 10 73 10 0 0 77 0 0 10 0 83 0 85 C 0 C 89 C 91 C 0 0 95 C 97 0 0 C LC 0

File output:

C 2 3 10 5 C 7 C 0 10 11 10 13 10 10 C 17 C 19 10 23 25 0 C 10 0 C 29 10 0 35 31 0 C 10 C 37 C 10 41 10 43 10 0 10 47 10 49 10 0 C 53 10 55 C C C 59 10 61 C C 10 65 C 67 C 10 10 71 C 73 10 0 0 77 C 79 10 0 C 83 10 85 C C C 89 10 91 C C 10 95 C 97 C 10 10 T 02 O 00